SyzygyData

Current Betti Table Entry:

$$q=0$$

0 1 2 3
0 3 8 6 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 (1,0,0) (2,1,0) (3,1,1) ·
1 · · · (3,3,3)
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·
0 1 2 3
0 1 1 1 ·
1 · · · 1
2 · · · ·

Schur Decomposition

Below is a plot displaying the Schur decomposition. In the $$\lambda=(\lambda_0,\lambda_1)$$ spot we place $$\beta_{1,\lambda}(2,1;2)$$, the multiplicity of $$\textbf{S}_{\lambda}$$ occuring in the decomposition of $$K_{1,0}(2,1;2)$$. Here $$\lambda$$ is the weight $$(\lambda_0,\lambda_1,\lambda_2)$$ where $$\lambda_2$$ is determined by the fact that $$|\lambda|$$ equals $$d(p+q)+b$$. The dominant weights are displayed in green. Click on an entry for more info!

1 2 3
0 · · ·
1 · ·
2 · · ·

Below is a plot displaying the multigraded Betti numbers. In the $$(a_0,a_1)$$ spot we place $$\beta_{1,\textbf{a}}(2,1;2)$$. Here $$\textbf{a}$$ is the weight $$(a_0,a_1,a_2)$$ where $$a_2$$ is determined by the fact that $$|\textbf{a}|$$ equals $$d(p+q)+b$$. Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!